Description

These functions evaluate the function rhypot(x, y), defined by rhypot(x, y) =
1 / hypot(x, y), for an entire vector of values at once. The
first parameter specifies the number of values to compute. Subsequent parameters specify
the argument and result vectors. Each vector is described by a pointer
to the first element and a stride, which is the increment between
successive elements.

These functions are not guaranteed to deliver results that are identical to
the results of evaluating 1.0 / hypot(x, y) given the same arguments.
Non-exceptional results, however, are accurate to within a unit in the last
place.

Usage

The element count *n must be greater than zero. The strides for
the argument and result arrays can be arbitrary integers, but the arrays
themselves must not be the same or overlap. A zero stride effectively
collapses an entire vector into a single element. A negative stride causes a
vector to be accessed in descending memory order, but note that the
corresponding pointer must still point to the first element of the vector
to be used; if the stride is negative, this will be the
highest-addressed element in memory. This convention differs from the Level 1 BLAS, in
which array parameters always refer to the lowest-addressed element in memory even
when negative increments are used.

These functions assume that the default round-to-nearest rounding direction mode is in
effect. On x86, these functions also assume that the default round-to-64-bit rounding
precision mode is in effect. The result of calling a vector function
with a non-default rounding mode in effect is undefined.

These functions handle special cases and exceptions in the spirit of IEEE
754. In particular,

if x or y is ±Inf, rhypot(x, y) is +0, even if the other of x or y is NaN,

if x or y is NaN and neither is infinite, rhypot(x, y) is NaN

if x and y are both zero, rhypot(x, y) is +0, and a division-by-zero exception is raised.

An application wanting to check for exceptions should call feclearexcept(FE_ALL_EXCEPT) before calling
these functions. On return, if fetestexcept(FE_INVALID | FE_DIVBYZERO | FE_OVERFLOW | FE_UNDERFLOW)
is non-zero, an exception has been raised. The application can then examine
the result or argument vectors for exceptional values. Some vector functions can
raise the inexact exception even if all elements of the argument array
are such that the numerical results are exact.